To find the missing exponent in the equation [tex]\(5.6 \times 10^{\square} = 56000\)[/tex], we can follow these steps:
1. Consider the given equation:
[tex]\[
5.6 \times 10^{x} = 56000
\][/tex]
2. Isolate [tex]\(10^{x}\)[/tex] by dividing both sides of the equation by 5.6:
[tex]\[
10^{x} = \frac{56000}{5.6}
\][/tex]
3. Simplify the right-hand side by performing the division:
[tex]\[
\frac{56000}{5.6} = 10000
\][/tex]
4. Now, our equation looks like:
[tex]\[
10^{x} = 10000
\][/tex]
5. Recognize that we need to find the exponent [tex]\(x\)[/tex] such that [tex]\(10\)[/tex] raised to this exponent equals [tex]\(10000\)[/tex].
6. Recall that:
[tex]\[
10000 = 10^4
\][/tex]
7. Therefore, the exponent [tex]\(x\)[/tex] that satisfies the equation is:
[tex]\[
x = 4
\][/tex]
Hence, the missing exponent in the equation [tex]\(5.6 \times 10^{\square} = 56000\)[/tex] is [tex]\(\boxed{4}\)[/tex].
